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C₄×#3584 #10574170

• p-group
• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

10396 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 36 points:

(1,2,3,4);(5,6)(7,16)(8,13)(9,14)(10,23)(11,15)(12,18)(17,30)(19,26)(20,28)(21,29)(22,33)(24,27)(25,32)(31,36)(34,35);(5,7)(6,12)(8,17)(9,18)(10,24)(11,19)(13,25)(14,26)(15,27)(16,23)(20,31)(21,32)(22,34)(28,35)(29,36)(30,33);(5,8)(6,13)(7,17)(9,21)(10,22)(11,20)(12,25)(14,29)(15,28)(16,30)(18,32)(19,31)(23,33)(24,34)(26,36)(27,35);(8,20)(13,28)(17,31)(21,22)(25,35)(29,33)(30,36)(32,34);(5,9,11,10)(6,14,15,23)(7,18,19,24)(8,21,20,22)(12,26,27,16)(13,29,28,33)(17,32,31,34)(25,36,35,30)

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10481366);